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3 machines have a productivity ratio of 1 to 2 to 5. All 3

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3 machines have a productivity ratio of 1 to 2 to 5. All 3 [#permalink] New post 16 Feb 2011, 03:34
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3 machines have a productivity ratio of 1 to 2 to 5. All 3 machines are working on a job for 3 hours. At the beginning of the 4th hour, the slowest machine breaks. It is fixed at the beginning of hour seven, and begins working again. The job is done in nine hours. What was the ratio of the work performed by the fastest machine as compared to the slowest?

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15/2

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Re: Ratio & Proportion [#permalink] New post 16 Feb 2011, 06:50
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3 machines have a productivity ratio of 1:2:5. all 3 machines are working on a job for 3 hours. at the beginning of the 4th hour, the slowest machine breaks. it is fixed at the beginning at hour 7, and begins working again. the job is done in 9 hours. what was the ratio of the work performed by the fastest machine to the work performed by the slowest?

"3 machines have a productivity ratio of 1:2:5" means that in a time interval (1 hour, 1 year, ...) the first machine can produce 1 part (so it's the slowest one), the second can produce 2 parts and the third and fastest one can produce 5 parts.

Now, the fastest machine worked for whole 9 hours thus produced 9*5=45 parts but the slowest machine worked only for 6 hours thus produced 6*1=6 parts, so the ratio of the work performed by the fastest machine to the work performed by the slowest is 45/6=15/2.
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Re: Ratio & Proportion [#permalink] New post 11 Aug 2011, 05:02
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ruturaj wrote:
please explain how slowest machine works for 6 hours


slowest machine worked
1st hour
2nd hour
3rd hour
Got broken
got fixed and returned to work at the beginning of the 7th hour so:
7th hour
8th hour
9th hour

Total of 6 hours.

So the slowest machine made 6 pieces, while the fastest machine made 45
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Re: Ratio & Proportion [#permalink] New post 16 Feb 2011, 03:49
1:2:5

Let's consider 1 work is done by the slowest machine in 1 hour.

in first 3 hours; Work performed by 3 machines
1*3:2*3:5*3

From beginning of 4th hour until start of 7th hour, 3 hours elapsed. Work performed by 3 machines
0:2*3:5*3. First one is 0 work as it is broken.

Job is done in nine hours; from start of 7th hour until end of 9th hour, 3 hours elapsed. Work performed by 3 machines
1*3:2*3:5*3

Total work performed by slowest machine: 3+3=6
Total work performed by fastest machine: 15+15+15=45

Ratio = 45/6 = 15/2

Ans: 15/2
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Re: Ratio & Proportion [#permalink] New post 17 Feb 2011, 11:45
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Re: Ratio & Proportion [#permalink] New post 11 Aug 2011, 04:27
please explain how slowest machine works for 6 hours
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Re: Ratio & Proportion [#permalink] New post 11 Aug 2011, 07:02
ruturaj wrote:
please explain how slowest machine works for 6 hours


3 machines have a productivity ratio of 1:2:5. all 3 machines are working on a job for 3 hours. at the beginning of the 4th hour, the slowest machine breaks. it is fixed at the beginning at hour 7, and begins working again. the job is done in 9 hours. what was the ratio of the work performed by the fastest machine to the work performed by the slowest?

Productivity ratio of 1:2:5 means;

In 1 hour:
Slowest machine just finishes 1 work
Medium fast machine finishes 2 work
Fastest machine finishes 5 work

3 hours work:
Slowest: 3*1=3 work
Medium: 3*2=6 work
Fastest: 3*5=15 work

THEN SLOWEST BREAKS.
It misses(3 hours):
4th hour
5th hour
6th hour

During which:
Medium fast completes: 3*2=6 work
Fastest completes: 3*5=15 work

Then
7th, 8th, 9th hour(3 hours)
Slowest: 3*1=3 work
Medium: 3*2=6 work
Fastest: 3*5=15 work

Work by fastest:Work by slowest
15+15+15:3+3
45:6
15:2
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Re: Ratio & Proportion [#permalink] New post 11 Aug 2011, 23:22
0-1 fastest = 5 slowest = 1
1-2----5----------1 ----
2-3 fastest = 5 ----1---

6-7----5--------1--
7-8----5---------1--
8-9----5---------1--

hence total = 45 and 6

thus 15/2
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Re: Ratio & Proportion [#permalink] New post 12 Aug 2011, 01:03
+1 for explanation..
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Re: Ratio & Proportion [#permalink] New post 21 Aug 2011, 09:37
let's suppose that in 1 hour each machine produces 1+2+5 = 8 units

in 3 hrs = 24 units
next 3 hrs = 21 units (slowest isnt working)
further 3 hrs = 24 untis

fastest worked for 9 hours, while the slowest worked for 6 hrs.

units produced by fastest / units produced by slowest = 9*5/6*1 = 15/2
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Re: Ratio & Proportion [#permalink] New post 21 Aug 2011, 13:29
Let M1 be the slowest and M3 be the fastest machine.

<---first 3 hours--><----3 hours----><---3 hours---->

M1 M1
M2 M2 M2
M3 M3 M3


productivity ratio = 1:2:5 (which is per hour)

x: 2x: 5x

work done by M3/ work done by M1 = (9*5x) / (6*x) = 45/6 = 15/2
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Re: Ratio & Proportion [#permalink] New post 02 Dec 2012, 21:49
The productivity ratio of the fastest machine to the slowest machine is 5:1.

The fastest machine worked for 9 straight hours. Thus, W = 5 x 9 = 45
The slowest machine brokedown in the 4th hour and was revived on the 7th hour. Thus, W = 1 x 6 = 6

The Output Ratio of fastest to slowest is 45 is to 6 ==> 15 : 2
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Re: 3 machines have a productivity ratio of 1 to 2 to 5. All 3 [#permalink] New post 27 Jun 2014, 06:37
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Re: 3 machines have a productivity ratio of 1 to 2 to 5. All 3   [#permalink] 27 Jun 2014, 06:37
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